谐和激励下单边碰撞系统的同宿分岔

摘要

研究了谐和激励下带平方非线性项的单边碰撞系统的同宿分岔.利用动力系统稳定性理论和Melnikov方法,分析了单边碰撞系统的同宿分岔,得到了系统出现Smale马蹄混沌的阀值.通过稳定与不稳定流形等数值仿真,对解析结果进行了验证和分析.%Chaos in a square-term non-linear vibro-impact system is investigated. Based on dynamical theory and Melnikov method,homoclinic bifurcation is studied and the critical value of onset of chaos is given analytically. Additively, numerical simulations about stable and unstable manifolds confirm the validity of analytic results.